I recall hearing (I think it on the Appendices) that PJ approached the TE for some sort of collaboration on the films, but he was simply ignored.

That, and the fact that CT has openly said he's averse to adaptations of his father's works, leads me to believe that he is, in fact, close-minded. He wants the books to be the beginning and the end of the matter.

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How do you know that he wouldn't have reacted positively to a different version of the films, created by a different director that better captured the spirit and tone of the films, from his perspective?

I don't know, but can deduce, that CT wouldn't have reacted positively to a different version of the films because of what I said above. He had the chance of collaborating with the production on LOTR, possibly even The Hobbit. There are lots of film adaptations nowadays where authors collaborate for a richer, truer adaptation of their works. If CT was supportive of one such, he would have done it.

My hope is that the TE will someday collaborate with a studio on an adaptation of The Silmarillion.

The Plan 9 Interview... in celebration of the 10th anniversary of the release of The Fellowship of the Ring.